Acoustic response in multi-domain based on least-square point collocation method and reproducing kernel particle method

作者：Li Hong Qiu^*; Chen Guo Ping; Shi Bao Jun

来源：Journal of Vibration and Shock, 2012, 31(8): 148-152+163.

• Acoustic response
• Analytic solution
• Approximated functions
• Boundary problems
• Collocation formulations
• Least square principle
• Least squares
• Mesh-less methods
• Multi domains
• Numerical example
• Numerical solution
• Point collocation method
• Reproducing kernel particle method
• System coefficients
• Two-dimensional problem

Meshless method faces several challenges, such as, boundary problems and stability of results. Here, approximated functions were constructed based on the principle of the reproducing kernel particle method and the least-square point collocation method was used to solve boundary problems. The system coefficient matrix generated with these methods was symmetric to ensure the results were stable. A least-square collocation formulation based on the reproducing kernel particle method was established for solving multi-domain acoustic response. Helmholtz equation was then discretized. To verify the proposed method, several numerical examples of two-dimensional problems were analyzed. Compared to analytic solutions to two examples, their numerical solutions computed with this meshless method were valid. This method did not need any initial mesh generation and mesh regeneration. Examples showed no matter how the points are distributed, uniformly or randomly, the results have good accuracy and convergence.

• 出版日期2012
• 单位南京航空航天大学